An analytical investigation is made of a precession-type instability which can occur in a flexibly supported aircraft-engine-propeller combination. By means of an idealized mathematical model which is comprised of a rigid power-plant system flexibly mounted in pitch and yaw to a fixed backup structure, the conditions required for neutral stability are determined. The paper also examines the sensitivity of the stability boundaries to changes in such parameters as stiffness, damping, and asymmetries in the engine mount, propeller speed, airspeed, Mach number, propeller thrust, and location of pitch and yaw axes. Stability is found to depend strongly on the damping and stiffness in the system. With the use of nondimensional charts, theoretical stability boundaries are compared with experimental results obtained in wind-tunnel tests of an aeroelastic airplane model. In general, the theoretical results, which do not account for wing response, show the same trends as observed experimentally; however, for a given set of conditions calculated airspeeds for neutral stability are consistently lower than the measured values. Evidently, this result is due to the fact that wing response tends to add damping to the system.